Exactly where is your difficulty?
Differentiate and equate to zero: .
We have: .
Yes, I think both end points, too. Critical points are only used for finding minima and maxima, so assuming you're finding the minimum or maximum over the range to , then you would need to include those points, too.
I suppose it could be that you're finding the minimum or maximum over a different range, and for some reason you're temporarily limiting yourself to finding critical points in the given range. That doesn't make much sense, though.